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Posterior contraction rates for the Bayesian approach to linear ill-posed inverse problems

Sergios Agapiou ; Stig Larsson (Institutionen för matematiska vetenskaper, matematik) ; Andrew M. Stuart
Stochastic Processes and their Applications (0304-4149). Vol. 123 (2013), 10, p. 3828–3860.
[Artikel, refereegranskad vetenskaplig]

We consider a Bayesian nonparametric approach to a family of linear inverse problems in a separable Hilbert space setting with Gaussian noise. We assume Gaussian priors, which are conjugate to the model, and present a method of identifying the posterior using its precision operator. Working with the unbounded precision operator enables us to use partial differential equations (PDE) methodology to obtain rates of contraction of the posterior distribution to a Dirac measure centered on the true solution. Our methods assume a relatively weak relation between the prior covariance, noise covariance and forward operator, allowing for a wide range of applications.

Nyckelord: Posterior consistency; Posterior contraction; Gaussian prior; Posterior distribution; Inverse problems

Denna post skapades 2013-07-13. Senast ändrad 2015-03-03.
CPL Pubid: 180135


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Institutionen för matematiska vetenskaper, matematik (2005-2016)


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